Current collectors in lithium-ion batteries are typically made from thin metal foils, such as aluminum for cathodes and copper for anodes. These foils undergo cyclic mechanical stresses during battery operation due to volume changes in active materials during charge and discharge cycles. Over time, this repetitive loading can lead to fatigue failure, compromising the structural integrity of the current collector and ultimately reducing battery performance and lifespan. Understanding and modeling this fatigue behavior is critical for improving battery durability.

Fatigue failure in metal foils is commonly analyzed using S-N curves (stress-life curves), which relate the amplitude of cyclic stress to the number of cycles until failure. For copper and aluminum foils, the S-N relationship can be approximated by the Basquin equation:
N = A (Δσ)^(-b)
where N is the number of cycles to failure, Δσ is the stress range, and A and b are material constants determined experimentally. Research on thin metal foils has shown that copper exhibits a higher fatigue resistance than aluminum under similar stress conditions due to its greater ductility. However, both materials experience accelerated fatigue degradation when subjected to higher stress amplitudes or when defects such as microcracks or impurities are present.

To account for variable amplitude loading in real-world battery applications, Miner’s rule is often employed. This linear damage accumulation model assumes that fatigue damage accumulates proportionally with each cycle, regardless of the sequence of stress levels. The total damage D is calculated as:
D = Σ (n_i / N_i)
where n_i is the number of cycles at a given stress level, and N_i is the number of cycles to failure at that stress level, derived from the S-N curve. Failure is predicted to occur when D ≥ 1.

Experimental studies on battery current collectors have demonstrated that fatigue cracks typically initiate at stress concentration sites, such as electrode coating edges or manufacturing defects. Finite element analysis (FEA) can be used to identify high-stress regions in the foil under simulated cycling conditions. For instance, a study on copper foils with a thickness of 10 μm revealed that stress concentrations near the edges of the anode coating could reduce the fatigue life by up to 30% compared to uniform loading scenarios.

The impact of mechanical strain on fatigue life is also influenced by the operating environment. Elevated temperatures, for example, can accelerate crack propagation due to thermal softening of the metal. In contrast, compressive stresses induced by electrode expansion may partially counteract tensile stresses during cycling, potentially extending fatigue life. However, this effect is highly dependent on the specific electrode composition and cycling conditions.

To mitigate fatigue-induced failures, design optimizations such as increasing foil thickness or introducing protective coatings can be considered. However, these approaches must balance mechanical robustness against other performance metrics, such as energy density and flexibility. Advanced modeling techniques, including multiscale simulations that couple electrochemical and mechanical effects, are increasingly being used to predict fatigue behavior more accurately.

In summary, modeling fatigue failure in foil current collectors requires a combination of empirical S-N data, damage accumulation theories like Miner’s rule, and detailed stress analysis. By understanding the factors that influence fatigue life, battery designers can develop more durable current collectors, ultimately enhancing the reliability and longevity of energy storage systems. Future research should focus on validating these models under realistic operating conditions and exploring the interactions between mechanical fatigue and other degradation mechanisms in batteries.